%% This is file `amsfonts.sty' generated from `amsfonts.doc'
%% on 3-SEP-1991 by the docstrip.ams utility (1.0). 
%%
%% This version modified for the `AMS Font Set in Type 1 format'
%% 
%%@texfile{%
%% filename="amsfonts.sty",
%% version="1.1a",
%% date="3-SEP-1991",
%% filetype="AMS-LaTeX: option",
%% copyright="Copyright (C) American Mathematical Society, all rights
%%   reserved.  Copying of this file is authorized only if either:
%%   (1) you make absolutely no changes to your copy, including name;
%%   OR (2) if you do make changes, you first rename it to some other
%%   name.",
%% author="American Mathematical Society",
%% address="American Mathematical Society,
%%   Technical Support Department,
%%   P. O. Box 6248,
%%   Providence, RI 02940,
%%   USA",
%% telephone="401-455-4080 or (in the USA) 800-321-4AMS",
%% email="Internet: Tech-Support@Math.AMS.org",
%% checksumtype="line count",
%% checksum="269",
%% codetable="ISO/ASCII",
%% keywords="latex, amslatex, ams-latex, amsfonts, msam, msbm, eufm,
%%   blackboard bold",
%% abstract="This file is part of the AMS-\LaTeX{} package, ver. 1.1.
%%   It is a \LaTeX{} option that provides a `newsymbol' command for
%%   defining math symbols from the two math symbol fonts in the
%%   AMSFonts (version 2.0+) font package. See the AMSFonts user's guide
%%   for more information. It also defines a command for producing
%%   `blackboard bold' letters (uppercase only)."
%%}
\expandafter\ifx\csname amsfonts.sty\endcsname\relax
\expandafter\def\csname amsfonts.sty\endcsname{}
\else\message{---already loaded}\endinput\fi
\def\filename{amsfonts.sty}
\def\fileversion{1.1a} \def\filedate{3-SEP-1991}
\immediate\write16{%
AMS-LaTeX option `\filename' (\fileversion, \filedate)}
%%% end of file header
\def\RIfM@{\relax\protect\ifmmode}
\def\boxz@{\box\z@}
\def\setboxz@h{\setbox\z@\hbox}
\def\wdz@{\wd\z@}
\def\noaccents@{\def\accentclass@{0}}
\def\Invalid@@{Invalid use of \string}
\def\nonmatherr@#1{\err@
    {\string#1\space allowed only in math mode}\@ehd}
\@ifundefined{err@}{\def\err@{\@latexerr}}{}
\new@mathgroup\msa@group
\new@mathgroup\msb@group
\define@mathgroup\mv@normal\msa@group{msa}{m}{n}
\define@mathgroup\mv@normal\msb@group{msb}{m}{n}
\define@mathgroup\mv@bold\msa@group{msa}{m}{n}
\define@mathgroup\mv@bold\msb@group{msb}{m}{n}
{\catcode`\"=12
\edef\@tempa{\hexnumber@\msa@group}%
\edef\@tempb{\hexnumber@\msb@group}%
\xdef\ulcorner{\delimiter"4\@tempa 70\@tempa 70 }
\xdef\urcorner{\delimiter"5\@tempa 71\@tempa 71 }
\xdef\llcorner{\delimiter"4\@tempa 78\@tempa 78 }
\xdef\lrcorner{\delimiter"5\@tempa 79\@tempa 79 }
\xdef\yen      {\noexpand\mathhexbox\@tempa 55 }
\xdef\checkmark{\noexpand\mathhexbox\@tempa 58 }
\xdef\circledR {\noexpand\mathhexbox\@tempa 72 }
\xdef\maltese  {\noexpand\mathhexbox\@tempa 7A }
\xdef\widehat#1{\noexpand\setboxz@h{$\noexpand\m@th#1$}%
 \noexpand\ifdim\noexpand\wdz@>\tw@ em\mathaccent"0\@tempb5B{#1}%
 \noexpand\else\mathaccent"0362{#1}\noexpand\fi}
\xdef\widetilde#1{\noexpand\setboxz@h{$\noexpand\m@th#1$}%
 \noexpand\ifdim\noexpand\wdz@>\tw@ em\mathaccent"0\@tempb5D{#1}%
 \noexpand\else\mathaccent"0365{#1}\noexpand\fi}
\global\mathchardef\dabar@="0\@tempa39
\xdef\dashrightarrow{\mathrel{\dabar@\dabar@\mathchar"0\@tempa4B}}%
\xdef\dashleftarrow{\mathrel{\mathchar"0\@tempa4C\dabar@\dabar@}}%
\global\let\dasharrow\dashrightarrow
\gdef\newsymbol#1#2#3#4#5{%
    \@ifdefinable#1{%
       \edef\next@
         {\ifcase #2 \or
            \hexnumber@{\msa@group}\or
            \hexnumber@{\msb@group}\fi}%
       \ifx\next@\@empty
         \err@{\Invalid@@\newsymbol}\@ehd%
       \else
        \global\mathchardef#1"#3\next@#4#5
       \fi}}
}
\let\rightleftharpoons\undefined \newsymbol\rightleftharpoons 130A
\let\angle\undefined             \newsymbol\angle             105C
\let\hbar\undefined              \newsymbol\hbar              207E
\let\sqsubset\undefined          \newsymbol\sqsubset          1340
\let\sqsupset\undefined          \newsymbol\sqsupset          1341
\let\mho\undefined               \newsymbol\mho               2066
\let\Box\undefined      \newsymbol\Box 1203
\let\Diamond\undefined  \newsymbol\Diamond 1206
\let\leadsto\undefined  \newsymbol\leadsto 1320
\let\lhd\undefined      \newsymbol\lhd 1343
\let\unlhd\undefined    \newsymbol\unlhd 1345
\let\rhd\undefined      \newsymbol\rhd 1342
\let\unrhd\undefined    \newsymbol\unrhd 1344
\edef\Join{\mathrel{\mathchar"0\hexnumber@\msb@group 6F\mkern-13.8mu%
  \mathchar"0\hexnumber@\msb@group 6E}}
\def\frak{\protect\pfrak}
\def\pfrak{\RIfM@\expandafter\frak@\else
                 \expandafter\nonmatherr@\expandafter\frak\fi}
\newmathalphabet\frak@
\addtoversion{normal}\frak@{euf}{m}{n}
\addtoversion{bold}\frak@{euf}{b}{n}
\def\bold{\protect\pbold}
\def\pbold{\RIfM@\expandafter\bold@\else
                 \expandafter\nonmatherr@\expandafter\bold\fi}
\newmathalphabet*\bold@{cmr}{bx}{n}
\def\Bbb{\protect\pBbb}
\def\pBbb{\RIfM@\expandafter\Bbb@\else
                 \expandafter\nonmatherr@\expandafter\Bbb\fi}
\edef\Bbb@{\noexpand\use@mathgroup
          \expandafter\noexpand\csname =msb\endcsname
          \msb@group}
\def\goth{\family{euf}\selectfont\frak@}
\newbox\Mathstrutbox@
\setbox\Mathstrutbox@\null
\def\Mathstrut@{\copy\Mathstrutbox@}
\addto@hook\every@size{\setbox\z@\hbox{$\m@th($}%
        \ht\Mathstrutbox@\ht\z@
        \dp\Mathstrutbox@\dp\z@}
\newbox\strutbox@
\def\strut@{\copy\strutbox@}
\addto@hook\every@size{%
    \setbox\strutbox@\hbox{\lower.5\normallineskiplimit
         \vbox{\kern-\normallineskiplimit\copy\strutbox}}}
\def\big{\bBigg@\@ne}
\def\Big{\bBigg@{1.5}}
\def\bigg{\bBigg@\tw@}
\def\Bigg{\bBigg@{2.5}}
\def\bBigg@#1#2{%
   {%
    \hbox{$\left#2\vcenter to#1\big@size{}\right.%
                         \nulldelimiterspace\z@ \m@th$}}}
\addto@hook\every@size{\setbox\z@\vbox{\hbox{$($}\kern\z@}%
  \big@size 1.2\ht\z@}
\newdimen\big@size
\newdimen\ex@
\addto@hook\every@size{\ex@.2326\fontdimen5\textfont\@ne}
\newdimen\minaw@
\addto@hook\every@size{\minaw@11.11128\ex@}
\addto@hook\every@size{\jot\thr@@\ex@}
\newmuskip\dotsspace@
\dotsspace@1.5mu
\def\smash{\@ifnextchar[\@xsmash{\@xsmash[tb]}}
\def\@xsmash[#1]{\def\smash@{#1}%
  \ifmmode\expandafter\mathpalette\expandafter\mathsm@sh\else
        \expandafter\makesm@sh\fi}
\def\finsm@sh{\def\mb@t{\ht\z@\z@}\def\mb@b{\dp\z@\z@}%
   \expandafter\@tfor\expandafter\@tempa
         \expandafter:\expandafter=\smash@\do
      {\csname mb@\@tempa\endcsname}%
   \leavevmode\boxz@}
\def\default@mextra{\def\accentclass@{7}}
\extra@def{cmm}{\skewchar#1'177}{\noaccents@}
\extra@def{cmsy}{\skewchar#1'60}{\noaccents@}
\new@fontshape{msa}{m}{n}{%
   <5>msam5%
   <6>msam5 at 6pt%
   <7>msam7%
   <8>msam7 at 8pt%
   <9>msam10 at 9pt%
   <10>msam10%
   <11>msam10 at10.95pt%
   <12>msam10 at12pt%
   <14>msam10 at14.4pt%
   <17>msam10 at17.28pt%
   <20>msam10 at20.74pt%
   <25>msam10 at24.88pt}{}
\extra@def{msa}{}{}
\new@fontshape{msb}{m}{n}{%
   <5>msbm5%
   <6>msbm5 at 6pt%
   <7>msbm7%
   <8>msbm7 at 8pt%
   <9>msbm10 at 9pt%
   <10>msbm10%
   <11>msbm10 at10.95pt%
   <12>msbm10 at12pt%
   <14>msbm10 at14.4pt%
   <17>msbm10 at17.28pt%
   <20>msbm10 at20.74pt%
   <25>msbm10 at24.88pt}{}
\extra@def{msb}{}{\noaccents@}
\new@fontshape{euf}{m}{n}{%
   <5>eufm5%
   <6>eufm5 at 6pt%
   <7>eufm7%
   <8>eufm7 at 8pt%
   <9>eufm10 at 9pt%
   <10>eufm10%
   <11>eufm10 at10.95pt%
   <12>eufm10 at12pt%
   <14>eufm10 at14.4pt%
   <17>eufm10 at17.28pt%
   <20>eufm10 at20.74pt%
   <25>eufm10 at24.88pt}{}
\new@fontshape{euf}{b}{n}{%
   <5>eufb5%
   <6>eufb5 at 6pt%
   <7>eufb7%
   <8>eufb7 at 8pt%
   <9>eufb10 at 9pt%
   <10>eufb10%
   <11>eufb10 at10.95pt%
   <12>eufb10 at12pt%
   <14>eufb10 at14.4pt%
   <17>eufb10 at17.28pt%
   <20>eufb10 at20.74pt%
   <25>eufb10 at24.88pt}{}
\extra@def{euf}{\hyphenchar#1\m@ne
       \@tempdima\fontdimen2#1%
       \fontdimen3#1.4\@tempdima
       \fontdimen4#1.3\@tempdima}
      {\noaccents@}
\new@fontshape{cmm}{b}{it}{%
      <5>cmmib5%
      <6>cmmib5 at 6pt%
      <7>cmmib7%
      <8>cmmib7 at 8pt%
      <9>cmmib10 at 9pt%
      <10>cmmib10%
      <11>cmmib10 at10.95pt%
      <12>cmmib10 at12pt%
      <14>cmmib10 at14.4pt%
      <17>cmmib10 at17.28pt%
      <20>cmmib10 at20.74pt%
      <25>cmmib10 at24.88pt%
      }{}
\new@fontshape{cmsy}{b}{n}{%
      <5>cmbsy5%
      <6>cmbsy5 at 6pt%
      <7>cmbsy7%
      <8>cmbsy7 at 8pt%
      <9>cmbsy10 at 9pt%
      <10>cmbsy10%
      <11>cmbsy10 at10.95pt%
      <12>cmbsy10 at12pt%
      <14>cmbsy10 at14.4pt%
      <17>cmbsy10 at17.28pt%
      <20>cmbsy10 at20.74pt%
      <25>cmbsy10 at24.88pt%
      }{}
\def\unbracefonts@{\let\math@bgroup\@empty\let\math@egroup\@empty}
\def\operator@font{\mathgroup\z@}
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
\endinput
%% 
%% End of file `amsfonts.sty'.
